Mohammed Mahfoud

Alumni

Publications

Bayesian Symbolic Regression with Entropic Reinforcement Learning

Sida Li

Esmeralda S. Whitammer

Symbolic regression is the problem of finding an algebraic expression describing a stochastic dependence of a target variable on a set of in… (see more)puts. Unlike forms of regression that fit parameters assuming a fixed model structure, symbolic regression is a search problem over the space of expressions, represented, for example, as abstract syntax trees using a library of operators. Symbolic regression is typically used in settings with limited, noisy data in the natural sciences. However, searching for a single best-fitting expression fails to capture the epistemic uncertainty about the expression, which motivates a Bayesian perspective that enables uncertainty quantification and specification of natural priors to constrain the search space. In this work, we propose ERRLESS (Entropy-Regularized Reinforcement Learning for Expression Structure Sampling), a scalable approach for sampling from the posterior distribution over expressions given data using maximum-entropy reinforcement learning. ERRLESS learns a neural policy that constructs expressions sequentially by building up their abstract syntax trees. At convergence, the policy samples expressions from the posterior. At test time, expressions can be sampled by rollouts of this policy. We demonstrate that ERRLESS achieves competitive results on the Feynman benchmark while producing short and interpretable expressions. Additionally, we demonstrate that the mean of the posterior predictive approximated by ERRLESS achieves a high coefficient of determination (

2026-05-30

Conference on Uncertainty in Artificial Intelligence (poster)

doi.org

proceedings.mlr.press

Learning Decision Trees as Amortized Structure Inference

Mohammed Mahfoud

Ghait Boukachab

Michał Koziarski

Alex Hernández-García

Stefan Bauer

Yoshua Bengio

Nikolay Malkin